On the suboptimality of the p-version interior penalty discontinuous Galerkin method
We address the question of the rates of convergence of the p-version interior penalty discontinuous Galerkin method (p-IPDG) for second order elliptic problems with non-homogeneous Dirichlet boundary conditions. It is known that the p-IPDG method admits slightly suboptimal a-priori bounds with respe...
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| Format: | Article |
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Springer Netherlands
2009
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| Online Access: | https://eprints.nottingham.ac.uk/1128/ |
| _version_ | 1848790541676838912 |
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| author | Georgoulis, Emmanuil H. Hall, Edward Melenk, Jens Markus |
| author_facet | Georgoulis, Emmanuil H. Hall, Edward Melenk, Jens Markus |
| author_sort | Georgoulis, Emmanuil H. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We address the question of the rates of convergence of the p-version interior penalty discontinuous Galerkin method (p-IPDG) for second order elliptic problems with non-homogeneous Dirichlet boundary conditions. It is known that the p-IPDG method admits slightly suboptimal a-priori bounds with respect to the polynomial degree (in the Hilbertian Sobolev space setting). An example for which the
suboptimal rate of convergence with respect to the polynomial degree is both proven theoretically and
validated in practice through numerical experiments is presented. Moreover, the performance of p-
IPDG on the related problem of p-approximation of corner singularities is assessed both theoretically and numerically, witnessing an almost doubling of the convergence rate of the p-IPDG method. |
| first_indexed | 2025-11-14T18:14:15Z |
| format | Article |
| id | nottingham-1128 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:14:15Z |
| publishDate | 2009 |
| publisher | Springer Netherlands |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-11282020-05-04T20:26:46Z https://eprints.nottingham.ac.uk/1128/ On the suboptimality of the p-version interior penalty discontinuous Galerkin method Georgoulis, Emmanuil H. Hall, Edward Melenk, Jens Markus We address the question of the rates of convergence of the p-version interior penalty discontinuous Galerkin method (p-IPDG) for second order elliptic problems with non-homogeneous Dirichlet boundary conditions. It is known that the p-IPDG method admits slightly suboptimal a-priori bounds with respect to the polynomial degree (in the Hilbertian Sobolev space setting). An example for which the suboptimal rate of convergence with respect to the polynomial degree is both proven theoretically and validated in practice through numerical experiments is presented. Moreover, the performance of p- IPDG on the related problem of p-approximation of corner singularities is assessed both theoretically and numerically, witnessing an almost doubling of the convergence rate of the p-IPDG method. Springer Netherlands 2009 Article PeerReviewed Georgoulis, Emmanuil H., Hall, Edward and Melenk, Jens Markus (2009) On the suboptimality of the p-version interior penalty discontinuous Galerkin method. Journal of Scientific Computing . ISSN 0885-7474 (In Press) discontinuous Galerkin method interior penalty a priori error estimation p-version suboptimality. http://www.springerlink.com/content/g075179366551117/fulltext.pdf |
| spellingShingle | discontinuous Galerkin method interior penalty a priori error estimation p-version suboptimality. Georgoulis, Emmanuil H. Hall, Edward Melenk, Jens Markus On the suboptimality of the p-version interior penalty discontinuous Galerkin method |
| title | On the suboptimality of the p-version interior penalty
discontinuous Galerkin method |
| title_full | On the suboptimality of the p-version interior penalty
discontinuous Galerkin method |
| title_fullStr | On the suboptimality of the p-version interior penalty
discontinuous Galerkin method |
| title_full_unstemmed | On the suboptimality of the p-version interior penalty
discontinuous Galerkin method |
| title_short | On the suboptimality of the p-version interior penalty
discontinuous Galerkin method |
| title_sort | on the suboptimality of the p-version interior penalty
discontinuous galerkin method |
| topic | discontinuous Galerkin method interior penalty a priori error estimation p-version suboptimality. |
| url | https://eprints.nottingham.ac.uk/1128/ https://eprints.nottingham.ac.uk/1128/ |